Related papers: Nonvanishing of Kronecker coefficients for rectang…

By a theorem of D. Wigner, an irreducible unitary representation with non-zero $(\frak{g},K)$-cohomology has trivial infinitesimal character, and hence up to unitary equivalence, these are finite in number. We have determined the number of…

We prove for each integer $\ell\geq 1$ an unconditional upper bound for the size of the $\ell$-torsion subgroup $Cl_K[\ell]$ of the class group of $K$, which holds for all but a zero density set of number fields $K$ of degree $d\in\{4,5\}$…

Let $n \in \mathbb{N}_{\geq 2}$. We prove that for every $k \geq 4$ there exist uniform but non-homogeneous Steiner bundles on $\mathbb{P}^n$ of $k$-type with disconnected splitting type, and we further investigate almost-uniform Steiner…

A major research area in discrete geometry is to consider the best way to partition the $d$-dimensional Euclidean space $\mathbb{R}^d$ under various quality criteria. In this paper we introduce a new type of space partitioning that is…

Let $\lambda$ be a symplectic partition, denote Jord^{bp}($\lambda$) the set of even positive integers i which appear in $\lambda$, and let a map $\epsilon:Jord^{bp}(\lambda) \to {\pm 1}$. The generalized Springer's correspondence…

We generalize overpartitions to (k,j)-colored partitions: k-colored partitions in which each part size may have at most j colors. We find numerous congruences and other symmetries. We use a wide array of tools to prove our theorems:…

Let K be a simplicial complex with vertex set V = {v_1,..., v_n}. The complex K is d-representable if there is a collection {C_1,...,C_n} of convex sets in R^d such that a subcollection {C_{i_1},...,C_{i_j}} has a nonempty intersection if…

We show that the coefficients of decomposition into an irreducible components of the tensor powers of level $r$ symmetric algebra of adjoint representation coincide with the Verlinder numbers. Also we construct (for $sl(2)) the…

We compute the generating function of column-strict plane partitions with parts in {1,2,...,n}, at most c columns, p rows of odd length and k parts equal to n. This refines both, Krattenthaler's ["The major counting of nonintersecting…

Let $G/H$ be a reductive symmetric space of split rank $1$ and let $K$ be a maximal compact subgroup of $G$. In a previous article the first two authors introduced a notion of cusp forms for $G/H$. We show that the space of cusp forms…

This paper examines 8-dimensional Riemannian manifolds whose structure group reduces to ${SO(4)}_{ir}\subset GL(8,\mathbb R)$, the image of an irreducible representation of $SO(4)$ on $\mathbb R^8$. We demonstrate that such a reduction can…

If $[\lambda(j)]$ is a multipartition of the positive integer $n$ (a sequence of partitions with total size $n$), and $\mu$ is a partition of $n$, we study the number $K_{[\lambda(j)]\mu}$ of sequences of semistandard Young tableaux of…

In this note we present a complete analysis of finite dimensional representations of the Lie superalgebra sl(2|1). This includes, in particular, the decomposition of all tensor products into their indecomposable building blocks. Our…

We generalize Regev's result on a virtual character of $S_n$. Suppose that $\lambda$ and $\mu$ are integer partitions of $n$. For the associated irreducible character $\chi^\lambda$ of $S_n$, when $\chi^\lambda(\mu)\neq0$ we find another…

We obtained some sufficient and necessary conditions of existence of faithful irreducible representations of a soluble group $G$ of finite rank over a field $k$. It was shown that the existence of such representations strongly depends on…

Let $A$ be a finite-dimensional algebra over an algebraically closed field. The problem of constructing indecomposable $A$-modules inductively from simple ones by means of exact sequences - called accessibility - is the starting point of…

We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any…

We propose a new approach to study the Kronecker coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. We explain the limiting behavior and associated bounds in the context of the partition…

Irreducible representations of quantum groups $SL_q(2)$ (in Woronowicz' approach) were classified in J.Wang, B.Parshall, Memoirs AMS 439 in the~case of $q$ being an~odd root of unity. Here we find the~irreducible representations for all…

Given a partition $\lambda$ of a number $k$, it is known that by adding a long line of length $n-k$, the dimension of the associated representation of $S_{n}$ is an integer-valued polynomial of degree $k$ in $n$. We show that its expansion…